The main aim of this study is to obtain an optimum design point for fin geometry, so that heat transfer rate reaches to a maximum value in a constant fin volume. Effect of fin thicknesses ratio (tau), convection coefficient power index (m), profile power parameter (n), base thickness (delta) and fin material are evaluated in the fin optimization point for heat transfer rate, effectiveness and efficiency. It's assumed that the thickness of longitudinal fins varies with length in a special profile, so four different shapes (rectangular, convex, triangular and concave) are considered. In present study, temperature-dependent heat generation, convection and radiation are considered and an analytical technique based on the least square method is proposed for the solution methodology. Results show that by increasing the fin thicknesses ratio, maximum heat transfer rate decreases and Copper among the other materials has the most heat transfer rate in a constant volume. (C) 2015 Elsevier Ltd. All rights reserved.